Although a shooting like the one at Washington’s Navy Yard is shocking, we can’t say it’s surprising. We also know it’s only a question of when and where the next shooting will occur. Perhaps another school. Maybe another shopping mall or another movie theater. Or another military base.

This week, John Rosenthal, founder and chairman of Stop Handgun Violence, was despairing about the number of Americans who have died from guns since he erected his giant billboard along the Mass Pike back in 1995. Take a guess.

How about: More than 600,000. That’s as though everyone in Boston had perished from guns — suicides or murders or accidental deaths — over that period. More than half of annual gun deaths are suicides, but there are still more than 11,000 homicides a year. And yet our dysfunctional national political system hasn’t yet mustered the resolve to pass sensible gun legislation.

The first step, of course, should be passage of legislation like the Manchin-Toomey bill, which would close the federal law’s large loopholes by requiring background checks on all gun sales made at gun shows, over the Internet, or as the result of advertisements in a news publication.

“It is important to appreciate that change on this level doesn’t happen overnight,” says Dan Gross, president of the Brady Center to Prevent Gun Violence, who notes that it took six votes over seven years to pass the original Brady Bill.

Expanded background checks already enjoy majority support in the Senate; the problem is that such a bill doesn’t yet have the 60 votes needed to overcome a filibuster. Gross is confident those votes will come — and that when they do, the House will face strong pressure to follow suit.

“We can’t confidently predict the date, but it will happen when the American public brings its voice to bear,” he says.

To aid in that effort, a group of committed senators should take note of what former Wisconsin Senator William Proxmire did with the convention against genocide. Proxmire spoke about that treaty every single Senate-session day for 20 years. Think of the effect it could have if a handful of senators spoke on the Senate floor every day or week about the latest victims of gun violence in this country.

But to increase the odds of the background check system flagging people like Navy Yard gunman Aaron Alexis and the other alienated, mentally ill men who so often commit public shootings, the law needs to be expanded to include as a reason for rejection — or at least a delay pending further investigation — concerns from credible public agencies or medical authorities about mental illness or instability. Although Alexis wasn’t prosecuted after either of his two arrests for discharging a gun, police investigators in Seattle and Forth Worth had ample reason to suspect he was mentally unstable.

In a different context, so did the Newport, R.I., police. Alexis had told them in early August that harassers were speaking to him through the wall of his hotel room and using “some sort of a microwave machine” to shoot vibrations through the ceiling to keep him awake.

The initial focus has been on how Alexis was allowed to keep his Navy security clearance. But this case highlights an equally important issue: Under current law, Alexis was able to pass a background check and buy the shotgun with which he started his shooting spree at the Washington Navy Yard. Lawmakers need to face this reality: A failure to take mental illness into fuller account leaves the door wide open for carnage that could be prevented.

Finally, if the federal government or the various states were to require gun owners to have liability insurance before buying a firearm, that would add an important private-sector safeguard. Such a requirement would probably discourage some mentally ill would-be shooters from even trying to purchase a gun; others wouldn’t find an insurer who would issue a policy.

Dismaying as these tragedies are, and discouraging as the slow progress is, those who favor reasonable gun laws can’t give up. Each new tragedy must spur them to greater efforts — on both the national and state levels.

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